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Cooperative Games: Core and Shapley Value

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  • Roberto Serrano

Abstract

This article describes the basic elements of the cooperative approach to game theory, one of the two counterparts of the discipline. After the presentation of some basic definitions, the focus will be on the core and the Shapley value, two of the most central solution concepts in cooperative game theory.

Suggested Citation

  • Roberto Serrano, 2007. "Cooperative Games: Core and Shapley Value," Working Papers wp2007_0709, CEMFI.
    • Handle: RePEc:cmf:wpaper:wp2007_0709
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    1. Perry, Motty & Reny, Philip J, 1994. "A Noncooperative View of Coalition Formation and the Core," Econometrica, Econometric Society, vol. 62(4), pages 795-817, July.
    2. Roberto Serrano, 2004. "Fifty Years of the Nash Program, 1953-2003," Working Papers 2004-20, Brown University, Department of Economics.
    3. Perez-Castrillo, David & Wettstein, David, 2001. "Bidding for the Surplus : A Non-cooperative Approach to the Shapley Value," Journal of Economic Theory, Elsevier, vol. 100(2), pages 274-294, October.
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    5. Herbert E. Scarf, 1965. "The Core of an N Person Game," Cowles Foundation Discussion Papers 182R, Cowles Foundation for Research in Economics, Yale University.
    6. Krishna, Vijay & Serrano, Roberto, 1995. "Perfect Equilibria of a Model of N-Person Noncooperative Bargaining," International Journal of Game Theory, Springer;Game Theory Society, vol. 24(3), pages 259-272.
    7. Perez-Castrillo J. David, 1994. "Cooperative Outcomes through Noncooperative Games," Games and Economic Behavior, Elsevier, vol. 7(3), pages 428-440, November.
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    9. Winter, Eyal, 1994. "The Demand Commitment Bargaining and Snowballing Cooperation," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 4(2), pages 255-273, March.
    10. Serrano, Roberto & Volij, Oscar, 1998. "Axiomatizations of neoclassical concepts for economies," Journal of Mathematical Economics, Elsevier, vol. 30(1), pages 87-108, August.
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    15. Anderson, Robert M, 1978. "An Elementary Core Equivalence Theorem," Econometrica, Econometric Society, vol. 46(6), pages 1483-1487, November.
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    18. Aumann, Robert J, 1985. "An Axiomatization of the Non-transferable Utility Value," Econometrica, Econometric Society, vol. 53(3), pages 599-612, May.
    19. Hart, Sergiu & Mas-Colell, Andreu, 1996. "Bargaining and Value," Econometrica, Econometric Society, vol. 64(2), pages 357-380, March.
    20. Roberto Serrano & Rajiv Vohra, 1997. "Non-cooperative implementation of the core," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 14(4), pages 513-525.
    21. Peleg, Bezalel, 1985. "An axiomatization of the core of cooperative games without side payments," Journal of Mathematical Economics, Elsevier, vol. 14(2), pages 203-214, April.
    22. Gul, Faruk, 1989. "Bargaining Foundations of Shapley Value," Econometrica, Econometric Society, vol. 57(1), pages 81-95, January.
    23. Geoffroy de Clippel & Hans Peters & Horst Zank, 2004. "Axiomatizing the Harsanyi solution, the symmetric egalitarian solution and the consistent solution for NTU-games," International Journal of Game Theory, Springer;Game Theory Society, vol. 33(1), pages 145-158, January.
    24. Moldovanu Benny & Winter Eyal, 1995. "Order Independent Equilibria," Games and Economic Behavior, Elsevier, vol. 9(1), pages 21-34, April.
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    Cited by:

    1. Messan Agbaglah, 2014. "A recursive core for cooperative games with overlapping coalitions," Cahiers de recherche 14-07, Departement d'économique de l'École de gestion à l'Université de Sherbrooke.
    2. Yusuke Kamishiro & Roberto Serrano, 2009. "Equilibrium Blocking in Large Quasilinear Economies," Working Papers wp2009_0911, CEMFI.
    3. Roberto Serrano, 2009. "On Watson's Non-Forcing Contracts and Renegotiation," Economics Bulletin, AccessEcon, vol. 29(3), pages 2350-2360.
    4. Rafael Repullo & Javier Suarez, 2008. "The Procyclical Effects of Basel II," Working Papers wp2008_0809, CEMFI.
    5. Max Bruche, 2009. "Bankruptcy Codes, Liquidation Timing, and Debt Valuation," Working Papers wp2009_0902, CEMFI.
    6. Joan Llull, 2008. "The Impact of Immigration on Productivity," Working Papers wp2008_0802, CEMFI.
    7. David Martinez-Miera & Rafael Repullo, 2010. "Does Competition Reduce the Risk of Bank Failure?," The Review of Financial Studies, Society for Financial Studies, vol. 23(10), pages 3638-3664, October.
    8. Yusuke Kamishiro & Roberto Serrano, 2009. "Equilibrium Blocking in Large Quasilinear Economies," Working Papers 2009-12, Brown University, Department of Economics.
    9. Manuel Arellano & Lars Peter Hansen & Enrique Sentana, 2009. "Underidentification? (Resumen)," Working Papers wp2009_0905, CEMFI.
    10. Serrano, Roberto & Vohra, Rajiv, 2010. "Multiplicity of mixed equilibria in mechanisms: A unified approach to exact and approximate implementation," Journal of Mathematical Economics, Elsevier, vol. 46(5), pages 775-785, September.
    11. Mustika, Alyssa Diva & Rigo-Mariani, Rémy & Debusschere, Vincent & Pachurka, Amaury, 2022. "A two-stage management strategy for the optimal operation and billing in an energy community with collective self-consumption," Applied Energy, Elsevier, vol. 310(C).
    12. Carlos Alberto Tovar Jaco & Madeleyne Karol Mucha Alhuay & Pedro Bernabe Venegas Rodriguez & Nivardo Alonzo Santill¨¢n Zapata & Jimmy Alberth Deza Quispe, 2021. "Analysis of Macroeconomic Determinants of Peruvian Gold Export Value in the Period 2003-2019," International Journal of Financial Research, International Journal of Financial Research, Sciedu Press, vol. 12(2), pages 43-54, April.
    13. Amal Abdel Razzac & Linda Salahaldin & Salah Eddine Elayoubi & Yezekael Hayel & Tijani Chahed, 2017. "A Game Theoretical Real Options Framework for Investment Decisions in Mobile TV Infrastructure," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 34(04), pages 1-34, August.
    14. Mêgnigbêto, Eustache, 2018. "Modelling the Triple Helix of university-industry-government relationships with game theory: Core, Shapley value and nucleolus as indicators of synergy within an innovation system," Journal of Informetrics, Elsevier, vol. 12(4), pages 1118-1132.

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